The X-ray CT (Computed Tomography) is a technology that conducts imaging of an observation object interior as a distribution of X-ray absorption coefficients based on projection data obtained by irradiating X-rays on observation objects.
Generally, the X-ray CT is configured for an X-ray tube and an X-ray detector to be disposed opposite to each other and a turn table is disposed in between. The rotation axis of this turn table is disposed to be orthogonal against the X-ray axis between the X-ray tube and the X-ray detector. In the X-ray CT device, CT tomographic images are reconstructed by processing the transmitted X-ray data from multiple angles against measuring object. Usually, transmitted X-ray data are gathered with equally spaced rotation by more than 180 degrees.
Heretofore, algorithms for enabling higher precision of X-ray CT reconstruction such as a technology for reconstitution of CT images of similar quality as of the conventional ones at a lower X-ray exposure dose, and another technology for reduction of metal artifacts have been studied. The aforementioned metal artifacts refers to a phenomenon in which an artificial noise is superimposed on reconstruction images as a consequence of reconstruction failure with precision when a measuring object contains a high X-ray absorption material with high density such as a metal. The X-ray CT reconstruction is a method to estimate a distribution of X-ray absorption coefficients of materials internally contained by obtaining the attenuation degree of the X-ray transmitted through a measuring object from projection images obtained under various projection angles. However, high X-ray absorption materials strongly attenuate the X-ray and the transmitted X-ray is lost in observation noises without practically being detected. Especially when the conventional filtered back projection method (FBP: Filtered Back Projection) is utilized, there is a problem that an accurate image reconstruction cannot be performed because of false image generation generally called as metal artifacts in the reconstruction images due to a fact that the FBP method is prone to the influence of noise. Although the FBP method is prone to the influence of noise as mentioned above, the main noise contains a shot noise that conforms to the Poisson distribution, and therefore the signal to noise ratio can be improved by intensifying the irradiation X-ray. By the method mentioned above, the relative noise influence can be made smaller and the image reconstruction accuracy can be improved. However, on the other hand, the radiation exposure dose is increased resulting in generation of probabilistic health risks such as carcinogenesis.
As has been mentioned thus far, the reduction of the X-ray exposure dose and the signal to noise ratio are in the trade-off relationship and a statistical inference method is proposed as a technology to obtain reconstruction images with a signal to noise ratio similar to that of the conventional method at a lower X-ray exposure dose. The statistical inference method can reduce an ill-posedness of estimation in a low dose exposure by utilizing an accurate statistical characteristics of the observation process and the a priori knowledge regarding materials to be imaged. As a result, artifacts included in the reconstruction images can be reduced at the same X-ray intensity and resolution as at the conventional ones.
Currently, the filtered back projection (FBP: Filtered Back Projection), the main stream of the image reconstruction method, PCLIS (Projection Completion Method based on a Linear Interpolation in the Sinogram) and an improved PCLIS do not perform the statistical inference that allows the existence of stochastic observation noise or the probabilistic deviation from the deterministic observation model we assume. The statistical inference method is classified into roughly three methods that are the maximum likelihood estimation method (Maximum Likelihood Estimation: MLE), the maximum a posteriori estimation method and the Bayesian inference method.
The maximum likelihood estimation method (MLE) is a statistical inference method without setting a priori knowledge regarding reconstruction images that represent pixel-wise attenuation coefficients of the object, and the most likely reconstruction image is estimated in terms of the probabilistic observation model that expresses the stochastic observation process. The stochastic observation process expresses a stochastic fluctuation (shot noise) regarding the photon number of the transmitted X-ray and so on.
The MAP estimation method and the Bayesian inference method express a priori knowledge regarding estimation objects in the form of a probability model to be incorporated into estimation. Namely, the MAP estimation method and the Bayesian inference method conduct the estimation considering both the probability model regarding observation and the probability model regarding estimation objects. The estimation object in the case of X-ray CT is an X-ray absorption coefficient. Specifically, the maximum value of the posterior distribution of the X-ray absorption coefficient calculated by the probability model regarding observation and the probability model regarding X-ray absorption coefficients of the object for estimation are set to be the estimated value in the MAP estimation method and the expected value in the posterior distribution of the same X-ray absorption coefficients is set to be the estimated value in the Bayesian inference method. While the MAP estimation method conducts estimation by choosing only one point that provides the maximum value of the posterior distribution, the Bayesian inference method chooses the expected value of the posterior distribution and conducts estimation by an average against the group of the X-ray absorption coefficients that widen the posterior distribution, accordingly. The point that gives the maximum of the posterior distribution can fluctuate sensitively corresponding to an observation noise and accordingly the Bayesian inference method provides more stable and higher precision estimation because the expected value of the posterior distribution is not so much influenced by the observation noise.
Here, the ordinary X-ray CT algorithms mostly estimate a single absorption coefficient for each pixel assuming that the incident X-ray consists of a line spectrum and/or the attenuation coefficient for each pixel does not depend on the spectrum of the incident X-ray. However, the actual X-ray does not consist of a single energy electromagnetic wave but a wave consisting of an energy spectrum continuously distributed toward lower energy starting with a maximum energy determined by the X-ray tube voltage. Also the real materials have energy-dependent attenuation coefficients. Due to these facts, the X-ray of higher energy is transmitted with little absorption when irradiated on a material. However, the attenuation of the lower energy X-rays occurs extensively and a phenomenon called beam hardening in which the X-ray spectral distribution after transmission through a material shifts to a higher energy region occurs.
The phenomena originating in the influence of energy dependence (wavelength dependence) of the X-ray absorption coefficients of a material cannot be correctly expressed by the observation process model wherein the X-ray source consists of a line spectrum and the energy dependence (the wavelength dependence) of X-ray absorption coefficients of a material is not considered, and the incorrect estimation would resultantly induce the beam hardening artifacts. The beam hardening artifacts are generated, in this manner, by an estimation based on the model not considering the energy dependence (the wavelength dependence) of the X-ray absorption coefficient of a material.
In particular, it is known that the striate artifacts called streak artifacts and dark band artifacts wherein X-ray absorption coefficients in the vicinity of high absorption materials are estimated to be lower than the actual value are generated, and this is thought to be remarkably influenced by not considering the influence of the beam hardening.
This phenomenon is explained below.
The X-ray is substantially attenuated when an X-ray is transmitted through high absorption materials such as metals with very high X-ray absorption coefficients. If the character of the high absorption material is expressed by an observation model, it would be presumed that a material with a high X-ray absorption coefficient exists in the vicinity of a high absorption material even with a model not considering the energy dependence (the wavelength dependence) of the X-ray absorption coefficient of the material. However, high energy X-rays transmit easily even when the material has high absorption characteristics. For this reason, some amount of the X-ray is observed even when the majority of photons having main energy corresponding to the X-ray source are absorbed during transmission through a high absorption material.
When high absorption materials exist at multiple separated positions, it is anticipated that the transmitted X-ray, the X-ray that transmits each of those multiple high absorption materials, is attenuated further extensively when materials with high X-ray absorption coefficients are overlapped according to a model that does not consider the energy dependence (the wavelength dependence) of the X-ray absorption coefficient. However, a certain amount of the high energy X-ray is practically observed even when the X-ray is transmitted through multiple high absorption materials. For this reason, a model that does not consider the energy dependence (the wavelength dependence) of the material X-ray absorption coefficient leads to a contradiction against an actual observation result under the assumption that a high absorption material simply exists. When X-ray absorption coefficients are estimated in such a manner that the observation model not considering the energy dependence of the X-ray absorption coefficient of the material contradicts with the actual observation result as little as possible, the dark band artifacts that estimate X-ray absorption coefficients near the high absorption material smaller than the actual values are generated.
A method to separate projection data into a metal region and a non-metal region and to subsequently reconstitute an image in each region, and then to overlap the thus obtained images is known as a method to reduce the metal artifacts. By conducting such a method, the inconsistency of the projection data in the metal region is corrected to reduce the metal artifacts generation. Also, the inventers of the present invention proposed an X-ray CT image processing method capable of reducing the metal artifacts by employing an X-ray CT image processing method that expresses the prior knowledge by a probability distribution characterized by the following parameters defined in the region of each pixel of the reconstruction image, the parameters being a parameter that expresses the existence rate for each tissue of the human body to be imaged, a parameter that expresses the X-ray absorption coefficient for each tissue and a parameter that expresses the spatial continuity extent of each tissue. (Refer to the patent literature 1)
However, the beam hardening artifacts generated by discrepancy between the actual observation process and the observation process not considering energy dependence of the X-ray absorption coefficient of the material has not been eliminated because these methods do not consider energy dependence (wavelength dependence) of the X-ray absorption coefficient.
And, a model considering the energy dependence (wavelength dependence) of the X-ray absorption coefficient as a method to reduce beam hardening artifacts is known. (Non-Patent Literatures 1 to 4) In the model that considers energy dependence (wavelength dependence) of the X-ray absorption coefficient, it is necessary to presume the X-ray absorption coefficient for each X-ray energy level. This leads to generation of ill-posedness as an estimation problem although the estimation problem is based on more accurate physical process. For example, let us consider a problem of estimating X-ray absorption coefficients at two kinds of energy levels by discretizing the X-ray energy for simplification purpose. In such case, the X-ray absorption coefficients to be estimated are increased by twofold compared with that under a conventional assumption even when the observed projection image is the same as the conventional one. Consequently, multiple solutions that do not clearly contradict the actual observation can be generated due to the increase of the degree of freedom for X-ray absorption coefficients. In this case, the estimation result is unstable because the result is sensitively influenced by the subtle observation noise. Thus, a constraint to suppress the degree of freedom of the X-ray absorption coefficient is necessary. Firstly in the non-patent literatures 1 to 3, the energy dependence (wavelength dependence) of the material is expressed by expressing the absorption coefficient depending on the energy at each pixel by weighted sum of the absorption coefficient energy function. The energy dependence (the wavelength dependence) of the X-ray absorption coefficient tends to be attenuated when the energy becomes higher though the extent of this tendency differs according to the material, which is common among each different material. When the X-ray energy is set as an input variable and the function that outputs the X-ray absorption coefficient at that X-ray energy is called the absorption coefficient function, the absorption coefficient function of any material is well expressed by a weighted sum (base function expression) of absorption coefficient functions for a few, typically two, materials because the absorption coefficient functions of different materials are similar to each other.
For example, the material class is determined based on the image obtained by FBP and the image reconstruction is performed based on that knowledge according to the non-patent literature 2. Estimation is performed under the assumption that the X-ray absorption coefficient for each pixel can be expressed by a combination of X-ray absorption coefficients specified for each known material class, as depicted in non-patent literature 4.
In this manner, the method to consider energy dependence (wavelength dependence) of X-ray absorption coefficient has been performed by reducing the degree of freedom of estimation parameters by utilizing a base function expression based on the wavelength dependence of the X-ray absorption coefficient for known material so that the ill-posedness can be suppressed. However, a problem that the constraint imposed is too strong is pointed out. To weaken the constraint, it is desired to represent the constraint in terms of the probabilistic model.
On the other hand, it has become possible, by the advent of DECT (Dual Energy Computed Tomography), to estimate the energy dependence (wavelength dependence) of materials based on the difference of X-ray absorption coefficients by filming at different X-ray tube voltages, from the hardware perspective. Various types of image reconstruction methods employing this DECT are known. (Non-Patent Literature 5 to 8) However, there are problems, one of which, for example, is that the image reconstruction method based on DECT generally requires a higher exposure dose than that of the monochromatic X-ray CT and the estimation accuracy becomes deteriorated when the exposure dose is constrained at that of the monochromatic X-ray CT. Also, the non-patent literature 5 describes a method to perform compensation by a subsequent image processing and thus there is a limit including a possibility of false images to be further generated.
The observation model not considering the energy dependence of the X-ray absorption coefficient of materials assumes that the X-ray consists only of a certain typical wavelength, not of multiple wavelengths. This can be considered to be the simplification of the process where the X-ray of multiple spectra is incident on a detector in a multiple manner. Such a phenomenon that the X-ray of multiple spectra is incident on a detector occurs not only in the spectrum space but also temporally and spatially. Namely, multiple X-rays are incident on the detector within a certain detection time and multiple X-rays are incident on a certain fixed area within the detection area. In the observation process where these projected X-rays are incident on the detector, further in a case where X-rays incident on the detector is represented by a single X-ray, a bias is generated in the estimation of the X-ray absorption coefficient in a similar manner where the beam hardening artifacts are generated when the energy dependence of the X-ray absorption coefficient is not considered. (Non-Patent Literature 9) That is to say, it is desirable to treat the projected X-ray to be incident on the detector as a sum of multiple X-rays assuming multiple beams not a single beam (not ignoring multiplicity of the X-ray) in the observation process.